That is not uncommon. Until that state starts actually reviewing and processing your "accepted" return, they won't have any record of it when you go to check status on their website. Accepted in TurboTax means they have received it. So as long as you see that next to your state return and not rejected, you are fine. Some states just take longer to process the returns.
The next step would be for them to review/process and approve your refund. Processing times vary from state to state. Patience is virtue when waiting on government to process returns.
You can go here
How do I track my state refund? select your state and most states have some type of note on their refund tracking page (the page where you enter your personal info to check status) that states how long processing may take. If there is no note there, no need to be alarmed.